The lines $ax + by + c = 0$,where $3a + 2b + 4c = 0$,are concurrent at the point:

Three lines $3x - y = 2$,$5x + ay = 3$,and $2x + y = 3$ are concurrent. Find the value of $a$.

If $a$ and $b$ are two arbitrary constants,then the straight line $(a - 2b)x + (a + 3b)y + 3a + 4b = 0$ will pass through

For the family of lines given by the equation $(2 + k)x + (1 + k)y = 5 + 7k$,which of the following statements is true for different values of $k$?

If the lines $ax + 2y + 1 = 0$,$bx + 3y + 1 = 0$,and $cx + 4y + 1 = 0$ are concurrent,then $a, b, c$ are in:

Let $C$ be the centroid of the triangle with vertices $(3, -1), (1, 3),$ and $(2, 4).$ Let $P$ be the point of intersection of the lines $x + 3y - 1 = 0$ and $3x - y + 1 = 0.$ Then the line passing through the points $C$ and $P$ also passes through the point